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This morning Ben Orlin gave the MAA Lecture for Students and Teachers, “Tic-Tac-Toe (or, What is Mathematics?)” as part of a day-long series of public lectures at the JMM. Orlin writes the blog Math With Bad Drawings, which was recently developed into a book of the same name. A charming high school math teacher with a knack for capturing poignant observations about math with google-eyed stick figures, his talk did not disappoint.

This morning, Karen Hunger Parshall talked about the flourishing world of mathematics post WWI in the Roaring Twenties in American Mathematics. Parshall framed the advances of the era through the bifurcation of topology into the point set branch, led by R.L. Moore, and the algebraic branch to Oswald Veblen, and a similar splits in other fields.

In the words of Dieudonne, this was a period of “development and chaos,” and unsurprisingly, the roaring 20’s of math was a whole bunch of white guys.

Benedict Gross kicked off his series of talks in the AMS Colloquium Lectures on Tuesday by speaking about the past, with a plan to reach the future of Number Theory by Friday. Gross, former MacArthur Fellow and winner of the Cole Prize in Number Theory is the George Vasmer Leverett Professor of Mathematics, Department of Mathematics, Harvard University. The series, entitled “Complex Multiplication: Past, Present, Future,” considers the interplay between imaginary quadratic fields and the theory of elliptic curves. The area “has a long and twisted history,” according to Gross. The first talk covered the two hundred years from 1751 to 1951, beginning with Euler reviewing Fagnano’s work on the lemniscate, and beginning his investigations of “elliptic integrals” of the form

\[\int\frac{dx}{\sqrt{ax^3+bx^2+cx+d}},\]

which lead to elliptic curves. Legendre and Gauss studied positive definite binary forms up to equivalence under the special linear group SL_2(Z). The number of equivalence classes of forms with a given discriminant is called the class number of the discriminant. The connection between these class numbers (and their modern variants) and elliptic curves becomes the story of complex multiplication.

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